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PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE

Author

Listed:
  • SHUHONG YU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • TINGSONG DU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

  • BO YU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

Abstract

As a generalization of the convex mappings, the generalized s-type preinvex mappings are firstly introduced. Their meaningful properties are then investigated and the Hermite–Hadamard-type integral inequalities via the newly proposed mappings in fractal space are developed. In accordance with the newly proposed identity with three parameters, it is interesting to present certain integral inequalities with regard to the mappings whose first-order derivatives in absolute value belong to the generalized s-type preinvexity. As applications, on the basis of local fractional calculus, certain inequalities in view of numerical integration, 𠜀-type special means, as well as moments of random variable, are acquired, respectively.

Suggested Citation

  • Shuhong Yu & Tingsong Du & Bo Yu, 2022. "PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-28, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501584
    DOI: 10.1142/S0218348X22501584
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